\section{Parameter Estimation}
\subsection*{Problem 3}
Bernoulli distribution
\[
f(\theta)=ln(\theta^{\left|T\right|}(1-\theta)^{\left|H\right|})=\left|T\right|ln(\theta)+\left|H\right|ln(1-\theta)
\]
\[
\frac{df}{d\theta}=\frac{\left|T\right|}{\theta}+\frac{\left|H\right|}{1-\theta}
\]
\[
\frac{df}{d\theta}=0\Rightarrow\frac{\left|T\right|}{\theta}+\frac{\left|H\right|}{1-\theta}=0
\]
\[
\frac{\left|T\right|}{\theta}+\frac{\left|H\right|}{1-\theta}=0\Rightarrow\theta=\frac{\left|T\right|}{\left|T\right|+\left|H\right|}
\]
